Let f(x) = x2 – 16 and g(x) = x + 4. find f/g and its domain.

a. x + 4; all real numbers except x ≠ –4
b. x – 4; all real numbers except x ≠ –4
c. x - 4; all real numbers except x ≠ 4
d. x + 4; all real numbers except x ≠ 4

The correct option is B, i.e., x – 4; all real numbers except x ≠ –4.

Explanation:

It is given that,

We have to find the function .

Using

Hence the fountain is (x-4).

The domain of is the intersection of domain of both function except the the values for which the value of denominator function 0.

Since the domain of f(x) and g(x) is all real numbers but the g(x) is 0 at x=-4, therefore the domain of is all real numbers except x ≠ –4.

Therefore, the correct option is B.

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